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Paradox Question
- Thread starter Asmodeus
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So many newbies lately! Here is a very important PSA about one of our most vital content policies! Read it even if you are an ancient member!
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Why does 0.999999... = 1
Pfft, proving that one is easy mode, you just need to use basic fractions.
(1/9) = 0.1111...
(1/9) x 9 = 0.1111... x 9
1 = 0.9999...
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The problem with proofs like this is that they have the same 'flaw' as the thing being proved... namely, the inexact approximation of a fraction with a decimal. That's exactly the issue people have with the original statement, so using it in your proof makes no sense.
I actually wrote a ridiculously long post on this question back on Oldguild, I might ask @Holmishire if he can find it....
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The problem with more complex proofs is that if people can't understand why the simple proofs make sense, then they probably don't know enough about math to understand the more accurate proofs. Most people can't really grasp the concept of infinitesimal differences (for similar reasons as why they can't really grasp the concept of infinity), so the only way to show them how it works is through wonky simple math like that. Same goes for the popular simple algebraic proof.
If I recall that post in question correctly, I think you showed the proof in the form of an infinite series. Most people don't even know what that is, much less understand how it works. There's really no good way to prove 1=0.999... to someone who doesn't already have a solid enough knowledge of math to have very likely already learned the proof.
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pls no
There's no search function on OldGuild archives. When I search for a particular quote, I am literally opening every individual day that each forum-list was open and scanning each thread listed.
The only reason this isn't so bad for my personal research is that I'm not looking for specific things—I'm looking for anything. So it is far easier to find useful information. I was just playing along with Rilla—if I do ever go look for his old roleplay, it won't be any time soon, and will be mostly a matter of personal challenge.
Oooh, I was just about to post that. That's what I'd always been taught.
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- Genres
- High fantasy is my personal favorite, followed closely by modern fantasy and post-apocalyptic, but I can happily play in any genre if the plot is good enough.
Wait. Hold up. I am majorly derailing this thread for a moment. I shall re-rail it as soon as my question is answered.
There's an archive?
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- Primarily Prefer Male
- No Preferences
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- High fantasy is my personal favorite, followed closely by modern fantasy and post-apocalyptic, but I can happily play in any genre if the plot is good enough.
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- Fantasy is my #1; I will give almost anything a chance if it has strong fantasy elements. Post apocalyptic, superhero, alternate history, science fantasy, some supernatural, romance, and a few fandoms (especially Game of Thrones) are also likely to catch my eye.
Not really. He's digging through saved pages on archive.org, if I recall correctly. It's extremely spotty rather than a full archive, so the odds of finding any specific thing you're searching for is pretty damned slim.
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The problem with more complex proofs is that if people can't understand why the simple proofs make sense, then they probably don't know enough about math to understand the more accurate proofs. Most people can't really grasp the concept of infinitesimal differences (for similar reasons as why they can't really grasp the concept of infinity), so the only way to show them how it works is through wonky simple math like that. Same goes for the popular simple algebraic proof.
If I recall that post in question correctly, I think you showed the proof in the form of an infinite series. Most people don't even know what that is, much less understand how it works. There's really no good way to prove 1=0.999... to someone who doesn't already have a solid enough knowledge of math to have very likely already learned the proof.
I did include the infinite series proof, but to some extent or another that still depends on the ill-defined "infinity" concept that causes the issue in the first place. I actually ended up going into the philosophy of maths and looking at the necessity of taking an axiomatic approach - which essentially boils down to "this is true because we define it to be true", which most people can understand.
I agree with what you're saying, don't get me wrong - but those sorts of proofs amount to tricking people into being comfortable with it, not actually proving anything. I was disputing that it was a proof, not that it can be useful :P
Ah, fair enough. I might try to track it down myself at some point.
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